Tatsuo Kobayashi

We study the modular symmetry in magnetized compactifications. The zero-modes with different Scherk–Schwarz phases transform one another. A generic model does not include modes with all the Scherk–Schwarz phases. Incomplete multiplet representations appear. The modular group is violated, but the modular symmetry still controls coupling terms in those models. Modular forms of the full symmetry appear as coupling constants.

A bstract: We clarify the structure of Yukawa couplings and mass matrices for matter fields in heterotic string theory on smooth Calabi-Yau threefolds with standard embedding. The topological structure of Calabi-Yau threefolds leads to interesting Yukawa textures that cannot be derived from group-theoretical symmetries, e.g., the so-called Weinberg texture in the case of two generations of matter fields. Furthermore, we find that a U (2) flavor symmetry, which plays an important role in controlling higher-dimensional operators in the Standard Model effective field theory, emerges at specific loci in the moduli space of multi-Higgs fields. Small perturbations around these loci generate semi-realistic patterns of quark masses and mixings.

The unsuppressed C P violation in QCD is a problem in the standard model. If we have some mechanism to guarantee real determinants of the quark mass matrices, the vanishing physical vacuum angle θ ¯ indicates the C P invariance at the fundamental level. Thus, the small θ ¯ is technically natural, since we have an enhanced C P symmetry in the limit of the vanishing θ ¯ = 0 . In fact, it was proved that the vacuum angle is never renormalized up to the four-loop level once it is fixed at 0 value at some high energy scale. The purpose of this paper is to construct a model that guarantees the real determinants of the quark mass matrices assuming a noninvertible symmetry. In the present model, we have only one C P violating phase and hence all observable phases such as phases in the Cabibbo-Kobayashi-Maskawa matrix, in the neutrino oscillation and in the leptogenesis are related. It should be remarkable that the correct sign of the baryon-number asymmetry in the present Universe is obtained and a narrow region for the C P violating phase δ CP ≃ 19 2 ° – 19 7 ° is predicted.

A bstract: We study the origin of modular weights of wave functions in magnetized T ² models. It is explicitly demonstrated that the modular weights of the wave functions on magnetized T ² are equivalent to their mass level. We further extend this result to magnetized T ^{2 g} models. As a result, we construct the wave functions of excited states in magnetized T ^{2 g} models and show that their modular weights are likewise equivalent to the corresponding mass levels.

We clarify selection rules of conjugacy classes of several finite discrete groups where we deal with both gauged and ungauged cases. We find that the selection rules enjoy finite Abelian or non-Abelian discrete symmetries originating from the inner and/or outer automorphism of underlying discrete groups. Since the selection rules of conjugacy classes do not obey conventional grouplike selection rules, they open up new coupling selection rules of fields which are labeled by the conjugacy classes.

A bstract: We investigate coupling selection rules in heterotic string theory on non-Abelian orbifolds. Since boundary conditions on the orbifolds are classified by conjugacy classes of space group elements, non-Abelian orbifolds give rise to non-invertible selection rules on couplings among twisted sectors as well as ones including untwisted sectors. Furthermore, we find that non-invertible selection rules lead to characteristic patterns of Yukawa matrices.

We propose a three-zero texture for the down-quark mass matrix within a S U ( 5 ) grand unified theory (GUT)-inspired Standard Model, enforced by a noninvertible selection rule originating from Z 2 gauging of Z N symmetries. Assuming C P invariance at the high-energy scale, our framework solves the strong C P problem while reproducing a realistic quark mass matrix. The C P symmetry is spontaneously broken down at an intermediate scale via complex vacuum expectation values of new scalar fields η i , which generate the C P phase in the Cabibbo-Kobayashi-Maskawa matrix without inducing the quantum chromodynamics (QCD) θ ¯ term. The present model incorporates three generations of matter, Higgs, and additional scalars with a common structure under the noninvertible symmetry, which may be naturally embedded into S O ( 10 ) GUTs at high energies.